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The dataset generation failed
Error code:   DatasetGenerationError
Exception:    TypeError
Message:      Couldn't cast array of type
struct<role: string, name: null, content: list<item: struct<model_identity: string, reasoning_effort: string, conversation_start_date: timestamp[s], knowledge_cutoff: string, channel_config: struct<valid_channels: list<item: string>, channel_required: bool>, type: string, instructions: string, text: string>>, channel: string, recipient: string>
to
{'role': Value('string'), 'name': Value('null'), 'content': List({'model_identity': Value('string'), 'reasoning_effort': Value('string'), 'conversation_start_date': Value('timestamp[s]'), 'knowledge_cutoff': Value('string'), 'channel_config': {'valid_channels': List(Value('string')), 'channel_required': Value('bool')}, 'type': Value('string'), 'instructions': Value('string'), 'text': Value('string')}), 'channel': Value('string')}
Traceback:    Traceback (most recent call last):
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/builder.py", line 1831, in _prepare_split_single
                  writer.write_table(table)
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/arrow_writer.py", line 714, in write_table
                  pa_table = table_cast(pa_table, self._schema)
                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2272, in table_cast
                  return cast_table_to_schema(table, schema)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2224, in cast_table_to_schema
                  cast_array_to_feature(
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 1795, in wrapper
                  return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
                                           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2052, in cast_array_to_feature
                  casted_array_values = _c(array.values, feature.feature)
                                        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 1797, in wrapper
                  return func(array, *args, **kwargs)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2002, in cast_array_to_feature
                  _c(array.field(name) if name in array_fields else null_array, subfeature)
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 1797, in wrapper
                  return func(array, *args, **kwargs)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2002, in cast_array_to_feature
                  _c(array.field(name) if name in array_fields else null_array, subfeature)
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 1797, in wrapper
                  return func(array, *args, **kwargs)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2052, in cast_array_to_feature
                  casted_array_values = _c(array.values, feature.feature)
                                        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 1797, in wrapper
                  return func(array, *args, **kwargs)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2092, in cast_array_to_feature
                  raise TypeError(f"Couldn't cast array of type\n{_short_str(array.type)}\nto\n{_short_str(feature)}")
              TypeError: Couldn't cast array of type
              struct<role: string, name: null, content: list<item: struct<model_identity: string, reasoning_effort: string, conversation_start_date: timestamp[s], knowledge_cutoff: string, channel_config: struct<valid_channels: list<item: string>, channel_required: bool>, type: string, instructions: string, text: string>>, channel: string, recipient: string>
              to
              {'role': Value('string'), 'name': Value('null'), 'content': List({'model_identity': Value('string'), 'reasoning_effort': Value('string'), 'conversation_start_date': Value('timestamp[s]'), 'knowledge_cutoff': Value('string'), 'channel_config': {'valid_channels': List(Value('string')), 'channel_required': Value('bool')}, 'type': Value('string'), 'instructions': Value('string'), 'text': Value('string')}), 'channel': Value('string')}
              
              The above exception was the direct cause of the following exception:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1450, in compute_config_parquet_and_info_response
                  parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
                                                                        ^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 993, in stream_convert_to_parquet
                  builder._prepare_split(
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/builder.py", line 1702, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/builder.py", line 1858, in _prepare_split_single
                  raise DatasetGenerationError("An error occurred while generating the dataset") from e
              datasets.exceptions.DatasetGenerationError: An error occurred while generating the dataset

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id
int64
question
string
origin_question
string
paths
list
responses
list
39
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
8. Given that $f(x)$ is a function defined on $\mathbf{R}$, and satisfies $f(x+2)[1-f(x)]=1+f(x), f(1)=$ 9997, then the value of $f(2009)$ is $\qquad$ .
[ "The functional equation can be written in a convenient form\n\n\\[\nf(x+2)=F\\!\\bigl(f(x)\\bigr), \\qquad \nF(y)=\\frac{1+y}{1-y}.\n\\]\n\nThus the values of \\(f\\) at arguments spaced by 2 are obtained by iterating the map \\(F\\).\n\n--------------------------------------------------------------------\n### 1. ...
[ { "request_id": "b371d4c51fbc4646bb5fa7a93043042a", "response_length": 152, "tokens_length": 27, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
50
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
Find all positive integers $n<1000$ such that the cube of the sum of the digits of $n$ equals $n^{2}$.
[ "Let \n\n\\[\ns=\\text{sum of the digits of }n .\n\\]\n\nThe condition is \n\n\\[\ns^{3}=n^{2}\\qquad\\Longrightarrow\\qquad n=\\sqrt{s^{3}}=s^{3/2}.\n\\]\n\nHence \\(s\\) must be a perfect square; write \\(s=k^{2}\\) for some integer \\(k\\ge1\\).\nThen \n\n\\[\nn=k^{3}\\qquad\\text{and}\\qquad \\text{sum of di...
[ { "request_id": "db3fc6815c34408ca06338cef63ff182", "response_length": 167, "tokens_length": 34, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
41
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
2. The sides of a convex quadrilateral are equal to $6, 7, 8, 9$ in some order. It is known that a circle can be inscribed in this quadrilateral and a circle can be circumscribed around it. Find the area of the quadrilateral.
[ "For a quadrilateral to have both an incircle (tangential) and a circumcircle (cyclic) the lengths of opposite sides must be equal in sum:\n\n\\[\na+c = b+d.\n\\]\n\nWith the four given side lengths \\(6,7,8,9\\) the only way to satisfy this is to pair \\(6\\) with \\(9\\) and \\(7\\) with \\(8\\):\n\n\\[\n6 + 9 = ...
[ { "request_id": "1b616f5d49864d22b3ca8d755d5cc8dc", "response_length": 159, "tokens_length": 30, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
58
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
If there is a point (-3, a) on the terminal side of the 600° angle, then the value of a is (  ) A: $-\sqrt{3}$ B: $-3\sqrt{3}$ C: $\pm\sqrt{3}$ D: $\pm3\sqrt{3}$
[ "The angle \\(600^\\circ\\) reduces to \\(240^\\circ\\) ( \\(600-360 = 240\\) ). \nFor a point \\((x,y)\\) on the terminal side of this angle we have \n\n\\[\n\\tan 240^\\circ = \\frac{y}{x}.\n\\]\n\nSince \\(\\tan 240^\\circ = \\tan(60^\\circ)=\\sqrt{3}\\),\n\n\\[\n\\frac{y}{x}=\\sqrt{3}\\quad\\Longrightarrow\\q...
[ { "request_id": "70d7b46ddcb049499ebd8da88620d020", "response_length": 150, "tokens_length": 26, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
24
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings? \[\begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair...
[ "The family containing Jim must share at least one trait (eye color or hair color) with each of the other two children in that family.\n\nCheck each answer choice:\n\n- **(A) Nadeen and Austin** – Jim (brown‑blond), Nadeen (brown‑black), Austin (blue‑blonde). \n No single eye color or hair color is common to all ...
[ { "request_id": "45e60359836d4ed69082097228c48d4a", "response_length": 169, "tokens_length": 30, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
77
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
5) An atoll has the shape of a circular crown delimited by two concentric circumferences with radii of $1 \mathrm{~km}$ and $6 \mathrm{~km}$, respectively. Giovanni and Marco are the only inhabitants of the atoll; after a storm that destroyed their huts, they decide to rebuild them as far apart as possible, but in such...
[ "To maximise the straight‑line distance between two huts we must choose two points on the annulus such that the segment connecting them stays entirely inside the annulus.\n\nLet the two points lie on the outer circle of radius \\(6\\) km, with a central angle \\(2\\alpha\\) between them. \nFor a chord of a circle ...
[ { "request_id": "1125056a860148f48db35c36c8f901e6", "response_length": 169, "tokens_length": 35, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
62
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
If the eccentricity of the ellipse $\dfrac{x^2}{4} + \dfrac{y^2}{m} = 1$ is $\dfrac{\sqrt{3}}{2}$, then the value of the real number $m$ is ______.
[ "For the ellipse \n\n\\[\n\\frac{x^{2}}{4}+\\frac{y^{2}}{m}=1\n\\]\n\nwe write it in standard form \n\n\\[\n\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1,\n\\qquad a^{2}=4,\\; b^{2}=m.\n\\]\n\nBecause \\(a^{2}=4\\) and \\(b^{2}=m\\), the major semi‑axis is \\(a=2\\) (provided \\(m<4\\); we will check consistency la...
[ { "request_id": "d219e8f13d36476d81b124a40d56c331", "response_length": 149, "tokens_length": 26, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
74
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
7. Regulation: For $x \in \mathbf{R}$, if and only if $n \leqslant x<n+1\left(n \in \mathbf{N}^{*}\right)$, then $[x]=n$. Then the solution set of the inequality $4[x]^{2}-36[x]+45 \leqslant 0$ is $\qquad$.
[ "The inequality involves the integer part \\([x]\\). \nLet \\([x]=n\\) where \\(n\\in \\mathbb N^{*}\\). \nThen we must solve \n\n\\[\n4n^{2}-36n+45\\le 0 .\n\\]\n\n---\n\n### 1. Solve the quadratic inequality\n\n\\[\n4n^{2}-36n+45=0\n\\]\n\n\\[\n\\Delta =(-36)^2-4\\cdot 4\\cdot 45 = 1296-720=576=24^{2}\n\\]\n\...
[ { "request_id": "4dddd11b4223461d93a86f2fd503d844", "response_length": 155, "tokens_length": 30, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
72
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
1. (16 points) There are two circles: one with center at point $A$ and radius 5, and another with center at point $B$ and radius 15. Their common internal tangent touches the circles at points $C$ and $D$ respectively. Lines $A B$ and $C D$ intersect at point $E$. Find $C D$, if $B E=39$.
[ "Let the tangent line be horizontal. \nTake \\(C=(x_1,0),\\; D=(x_2,0)\\) with \\(x_2>x_1\\). \nSince the radii are perpendicular to the tangent, the centers are\n\n\\[\nA=(x_1,5), \\qquad B=(x_2,-15).\n\\]\n\nThe segment \\(AB\\) meets the tangent line \\(CD\\) at \\(E\\). \nThe equation of line \\(AB\\) is\n\n...
[ { "request_id": "8c65ed4aa3334449bd3cfb8358e669f0", "response_length": 175, "tokens_length": 31, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid ...
21
### ROLE ### Your task is to act as a problem-solving expert. ### OBJECTIVE ### Analyze multiple independent solutions for a given mathematical problem and generate a final, and definitive answer. The final solution must be presented as your own standard, correct answer. ### CORE INSTRUCTIONS ### 1. **Analyze and Sy...
Given $i$ is the imaginary unit, the imaginary part of the complex number $1-2i$ is ( ) A: 2 B: 1 C: -1 D: -2
[ "\\boxed{D}", "The complex number is \\(1-2i\\). \nThe coefficient of \\(i\\) is \\(-2\\), which is the imaginary part.\n\n\\[\n\\boxed{D}\n\\]", "The complex number is \\(1-2i\\). \nIts imaginary part is the coefficient of \\(i\\), which equals \\(-2\\).\n\n\\[\n\\boxed{D}\n\\]" ]
[ { "request_id": "ab073245211641fda674c852f9be3e56", "response_length": 428, "tokens_length": 113, "is_truncated": 0, "response": "<|start|>system<|message|>You are ChatGPT, a large language model trained by OpenAI.\nKnowledge cutoff: 2024-06\nCurrent date: 2025-10-11\n\nReasoning: low\n\n# Valid...
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